Overview of Image Registration Methods

As image registration is used in different areas, such as remote sensing, medical imaging, computer vision etc., its application can be divided into four main groups (Brown, 1992):

• Multiview Analysis: Images of the same scene are acquired at different viewpoints. The aim is to gain a larger 2D view or a 3D representation of the scanned scene.

• Multitemporal Analysis: Images of the same scene are acquired at different time points and possibly under different conditions. Thus changes in the scene which appeared between consecutive image acquisitions can be found and evaluated.

• Multimodal Analysis: Images of the same scene are acquired by different sensors. The integration of the information obtained from different source streams to gain more complex and detailed scene representation is accomplished with this analysis.

• Scene to model registration: Images of a scene and a model of the scene are registered. The aim is to localize and compare the acquired image in the scene/model.

The image acquisition with the SBFSEM technique is classified as a multiview analysis. Because, as above described, images of the same scene are acquired at different viewpoints. Furthermore standard image registration algorithms are categorized into two main meth- ods: area based and feature based methods (Zitova and Flusser, 2003). In the following the original image is called reference image and the image to be mapped onto the reference image is referred to as the target image.

Area based registration is focused on the global structure of the image (Fonseca and Manjunath, 1996). Consequently this method is applied if the images do not contain many prominent details and the distinctive information is provided by graylevels/colors rather than by local shapes and structure. Therefore one principal limitation is, that reference and target image must have similar intensity functions (identical or at least statistically dependent). The second limitation is that only transformations in x-, y-direction and small rotations between images are located by the algorithm. One prominent representative of the area-based method is the normalized cross-correlation and its modifications (Pratt, 1974). The calculated normalized cross-correlation gives a measure of degree of similarity between the reference and target image. The maximum value indicates the pixel shift in x-, y- direction between the two images. Disadvantages are that the normalized cross-correlation is not invariant with respect to imaging scale, rotation, and perspective distortions. Further approaches of the area-based registration are Fourier methods and mutual information

3.2 Software - Neuron2D 21

methods, where a measurement of statistical dependency between images from different modalities is calculated (Viola and Wells, 1997). Fourier methods are used when images were acquired under varying conditions or are corrupted by frequency-dependent noise. One representative is the phase-correlation method (Kuglin and Hines, 1975), which is based on the Fourier Shift Theorem (Bracewell, 1965) and was originally proposed for the registration of translated images. It computes the cross-power spectrum of the sensed and reference image and looks for the location of the peak in its inverse:

(∆x,∆y) =argmax (x,y) F−1 F(I)F(T)∗ |F(I)F(T)∗_| (3.1)

where I = reference image and T = target image.

Such as in the normalized cross-correlation the peak indicates the pixel shift between the two images.

Feature based methods are the second main method of image registration algorithms (Zitova and Flusser, 2003). These are typically applied when the local structural informa- tion is more significant than the information carried by the image intensities. They allow registering of images of completely different nature (such as aerial photographs, maps) and can handle complex between-image distortions. The crucial point is to have discriminative and robust feature descriptors that are invariant to all assumed differences between the images. Features are for example significant regions, lines or points, which can be detected in both images. This kind of registration method is based on algorithms using spatial relations, invariant descriptors or relaxation approaches (Zitova and Flusser, 2003). By selecting appropriate features, feature based methods are very robust to image rotations and zooming.

Tiled image stacks acquired with the SBFSEM technique have the following properties: predefined arrangement of the image tiles (stored in image file name), user-defined overlap (2 - 10%) of successive images, possibly brightness changes, small translational shifts in x-, y-direction between images and no image rotations/zooming. To cover these requirements, I implemented for the image registration function the above decribed phase-correlation method, which estimates efficiently the translative movement between two images and is robust against brightness changes. The phase-correlation method has been chosen as for feature-based matching methods it is necessary to have significant local structural image information, which is not given for the small overlapping region of SBFSEM image stacks. Therefore a member of area-based methods is chosen, where image registration is based

22 3. Results

on image intensity values. Furthermore, the phase-correlation method is robust against frequency dependent noise and non-uniform, time varying illumination disturbances. As one of the advantages of SBFSEM is, that the lateral position jitter is less than 10 nm, only small translational shifts between subimage stacks are expected and those can be calculated with the used phase-correlation method.